This is a runnable sample for bearer token authentication in ASP.NET Core.
How to achieve a bearer token authentication and authorization in ASP.NET Core
At back end, you can generate the token following this code:
[Route("api/[controller]")]
public class TokenAuthController : Controller
{
    [HttpPost]
    public string GetAuthToken(User user)
    {
        var existUser = UserStorage.Users.FirstOrDefault(u => u.Username == user.Username && u.Password == user.Password);
        if (existUser != null)
        {
            var requestAt = DateTime.Now;
            var expiresIn = requestAt + TokenAuthOption.ExpiresSpan;
            var token = GenerateToken(existUser, expiresIn);
            return JsonConvert.SerializeObject(new {
                stateCode = 1,
                requertAt = requestAt,
                expiresIn = TokenAuthOption.ExpiresSpan.TotalSeconds,
                accessToken = token
            });
        }
        else
        {
            return JsonConvert.SerializeObject(new { stateCode = -1, errors = "Username or password is invalid" });
        }
    }
    private string GenerateToken(User user, DateTime expires)
    {
        var handler = new JwtSecurityTokenHandler();
        ClaimsIdentity identity = new ClaimsIdentity(
            new GenericIdentity(user.Username, "TokenAuth"),
            new[] {
                new Claim("ID", user.ID.ToString())
            }
        );
        var securityToken = handler.CreateToken(new SecurityTokenDescriptor
        {
            Issuer = TokenAuthOption.Issuer,
            Audience = TokenAuthOption.Audience,
            SigningCredentials = TokenAuthOption.SigningCredentials,
            Subject = identity,
            Expires = expires
        });
        return handler.WriteToken(securityToken);
    }
}
In Startup.cs/ConfigureServices method
services.AddAuthorization(auth =>
{
    auth.AddPolicy("Bearer", new AuthorizationPolicyBuilder()
        .AddAuthenticationSchemes(JwtBearerDefaults.AuthenticationScheme)
        .RequireAuthenticatedUser().Build());
});
And add this code in Configure method
app.UseJwtBearerAuthentication(new JwtBearerOptions {
    TokenValidationParameters = new TokenValidationParameters {
        IssuerSigningKey = TokenAuthOption.Key,
        ValidAudience = TokenAuthOption.Audience,
        ValidIssuer = TokenAuthOption.Issuer,
        ValidateIssuerSigningKey = true,
        ValidateLifetime = true,
        ClockSkew = TimeSpan.FromMinutes(0)
    }
});
At front end, you just add the token to header like this:  
$.ajaxSetup({
    headers: { "Authorization": "Bearer " + accessToken }
});
or  
$.ajax("http://somedomain/somepath/somepage",{
    headers:{ "Authorization": "Bearer " + accessToken },
    /*some else parameter for ajax, see more you can review the Jquery API*/
});